Predictability Prior Driven White-Box Transformer for $$$k$$$-Space Interpolation

Motivation: Existing $$$k$$$-space interpolation methods solely rely on local predictability while neglecting the dependency between missing data and the global $$$k$$$-space. Goal(s): We seek to construct a method that can simultaneously extract local and global predictable priors dependent on $$$k$$$-space to achieve accurate interpolation of missing data in $$$k$$$-space. Approach: We leverage globally predictable relationships in $$$k$$$-space to guide the development of an interpretable $$$k$$$-space Transformer unfolding model. Furthermore, this model incorporates the self-consistent prior of SPIRiT to characterize local predictability. Results: Our method outperforms both the SPIRiT model, which relies on local predictability priors, and the $$$k$$$-space convolutional neural network model. Impact: Drawing upon global and local predictability priors in $$$k$$$-space, we introduce, for the first time, a white-box Transformer for $$$k$$$-space interpolation. Our method exhibits enhanced interpretability and lower computational complexity compared to conventional Transformer, thereby presenting promising prospects.